Questions tagged [linear-systems]
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21
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Find the series {$a_i$}$_{i=-\infty}^{+\infty}$ - Linear system course
I have a question. this is sub-question D:
Let $T${$x(t)$}$ = \int_{-\infty}^{t} [x(\tau) - x(\tau - 1)]d\tau$.
Consider the signal $x_3(t) = a_i, \forall t \in (i,i+1]$ and $\forall i \in \mathbb{Z}$....
1
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why Type III systems has at least two gain margins?
I heard the following statement https://engineering.stackexchange.com/a/54322/40848
if we have a type III system, or one that has three or more low-frequency poles that we're closing around, then we ...
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Why are the phase indicators different between the open loop bode plot and the closed loop bode plot?
I have an open-loop transfer function G
num=105*conv([1 1],[1 2 43.25]);
den=conv([2 0 0],conv([1 2 82],[1 2 101]));
G=tf(num,den);
and a closed-loop function of G/(1+G). Here are the open-loop bode ...
- 19
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57
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What is the effect of the resonant frequency of the system function Porter diagram on the stability of the system and how to analyze it?
I am a novice in automatic control, the theoretical basis is not very good. We have a large electric clamping jaw, single degree of freedom, the motor is controlled by the torque output, the motor has ...
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74
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How to solve for discrete state space matrices given input and output
I have a set of time-series data that consists of inputs $u_k$ where $
u \in R $ and $k = 1 ... T$, and outputs $ y_k $ where $ y \in R^2 $ and also $k = 1 ... T$, from a given system. I believe this ...
- 31
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Estimating the effective area and temperature coeffecient of a solar panel
I have a bunch of solar panels, each one is connected to an inverter.
For each solar panel I have two sensors, a wind and a west sensor.
From every inverter, I collect the power output.
The readings ...
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64
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Looking for a linear actuator that can carry a transverse load? Does such a product exist?
I am looking for a product that works like a linear actuator where you can control how far it extends but it can also hold a transverse load at the furthest point of extension.
What I am looking for ...
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118
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Finding a signal output $y(n)$ with input signal $x(n)$ and impulse response $h(n)$ with a DTFT
I am studying for my Digital Signal Processing course and I am stucking on the following exercise:
Given an $\text{LTI}$-system with input signal $$x(n)=\frac{1}{4^n}u(n)$$
and impulse response $$h(n)...
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104
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Retractable linear mechanism with a retractable drive for servo control
I am considering a mechanical system that is able to retract and extend via servo control but with the drive mechanism being retractable itself. Doing so I will be able to have a multiplied retracting ...
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42
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Modelling a Simple Translational System
I posted this on stack exchange physics, sadly no one has answered so I thought I'd try my luck here.
I am trying to model the following translational mechanical system in I/O form, however I am ...
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130
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System identification of a simple motor with only position measurements
(Cross-posting from statistics stackexchange)
Say we have a permanent-magnet DC motor that roughly obeys the system equation
$$\ddot{x}(t) = \alpha \dot{x}(t) + \beta u(t) + \gamma $$
where $x(t)$ is ...
- 113
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Is it possible to calculate Over Shoot percentage and settling time of an Underdamped 2nd order system with Ramp input?
Most of the books derive Over Shoot percentage, settling time for 2nd order underdamped it for unit step response. Do these parameters exist for 2nd order underdamped system for Ramp response too?
If ...
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128
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Quality of the transient response for an arbitrary transfer function
The question is simple and I rather need a reference point.
How the parameters of transients are estimated (as in the picture) from an arbitrary linear transfer function (formula is given).
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Linear Nastran model not converging
I am running a SOL 101 linear statics FEA. If I fix down the whole geometry it converges. But anything less than around 90% fix down and it will sit there crunching away at the numbers forever. This ...
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Lyaponuv stability condition of linear systems for homogenous P in V(x) = x^T P x
I am currently learning about using Lyaponuv functions to find Linear Matrix Inequalities (LMIs) as conditions for stability of a linear time invariant system.
i.e.
$$
\dot{x}(t) = Ax(t)
$$
is stable ...
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158
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LQR control effort / control bandwidth relationship
I'm working with a linear system, having given matrices A and B
$$A = \left[\begin{array}{cc} 0 & 1 \\ -0.9 & 0 \end{array}\right]$$
$$B = \left[\begin{array}{c} 0 \\ 2 \end{array}\right]$$
...
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Feedback Control Question: Finding compensator numerator (B(s)) and denominator (A(s)) polynomials to satisfy a specific requirement
I wish to find the polynomials B(s) and A(s) in the following compensator equation:
A(s)D(s) + B(s)N(s) = F(s)
Given,
$$N(s) = s - 2$$
$$D(s) = s^2 - 1$$
$$F(s) = s^2 + 3*s + 4$$
Condition
The degree ...
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how do i formulate a kalman filter for an upwash coefficient?
I want to make a kalman filter that will estimate the upwash coefficient $C_{\alpha_{up}}$
my state vector: $ X_k=[u \ v \ w \ C_{\alpha_{up}} ]^T $
My measurement vector: $ Z_k =[\alpha_m \ \beta_m ...
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Minimal realization of a MISO system
Given the following system:
$$\dot{x} = \begin{bmatrix}1 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 1 \end{bmatrix}x + \begin{bmatrix}0 & 1 \\ 1 & 0 \\ 0 & 1 \end{bmatrix} u$$...
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Why is it impossible to create an observer for this not fully observable system?
Consider a 1D point-mass moving along an axis. A force $u$ is applied as control. There is no gravity or other forces involved. The system can be described in state space equations as:
$$\begin{align}...
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Controllability of $x' = Ax + Bu(t)$ implies controllability of $\left \{ \begin{matrix} x' = Ax + By \\ y'=u(t) \end{matrix} \right.$
Suppose that the system
$$x'(t)=Ax(t)+Bu(t)$$
is controllable in $\mathbb{R}^n$, where $A$ is $n \times n$, $B$ is $ n \times m$ and $u(t)$ is $m \times 1$
Show that the system
$$\left \{ \begin{...
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